Three fire engines and around 15 firefighters were called to a fire at a flat in Knowles Close, West Drayton.
Part of a first floor flat was damaged by fire.
A woman and child were rescued from the affected property by firefighters using a ladder. They were treated at the scene for smoke inhalation and taken to hospital by London Ambulance Service crews as a precaution.
Around 15 people left the building before the arrival of the Brigade.
The Brigade was called at 2113 and the fire was under control at 2154. Fire crews from Hayes, Hillingdon and Feltham fire stations attended the scene.
The cause of the fire is under investigation by the Brigade and the Metropolitan Police Service.